Passive optical resonators can be efficiently excited by laser light as its coherence allows for a constant phase relationship of the input laser light field with the field inside the resonator. Under proper resonance conditions, energy is continuously coupled to the enhancement cavity (EC), enabling a steady state in which the power circulating in the cavity can be several orders of magnitude larger than the input laser light power, the enhancement being limited by the resonator round trip losses and chromatic dispersion. The resonator is called stable if the field distribution of the intracavity light is repeated with each circulation in the resonator. Each resonator is characterized by a certain stability range (range of geometrical parameters). The stability range depends on the geometric properties of the mirror positions, like mirror distances and mirror inclinations relative to a resonator plane, and on optical properties, like focussing distances of the mirrors. At edges of the stability range, i.e. at the edges of the parameter ranges allowing a stable EC operation, slight changes of parameters, e. g. a slightly changing distance between mirrors can essentially impair or even completely deteriorate the coherent light enhancement. At different edges of the stability range, the resonator has different sensitivities to maladjustments and vibrations. If the operation close an edge of the stability range is desired, configurations of the resonator with low sensitivity to maladjustments are preferred.
As in general the efficiency of optical nonlinear processes increases with the driving intensity, the EC technique lends itself to the efficient conversion of laser light via intra-cavity nonlinear processes. The conversion of the fundamental intra-cavity light upon a pass through a nonlinear medium represents round trip losses, which can be adjusted according to the applying nonlinear law and under damage threshold constraints to reach an intensity in the nonlinear medium leading to an optimum of the net conversion (i.e. total converted power divided by input power).
Numerous applications of ECs for the efficient conversion of continuous-wave or pulsed radiation to its harmonics have been proposed (see overview by I. Pupeza, “Power Scaling of Enhancement Cavities for Nonlinear Optics”, Springer Theses, Springer N.Y., 2012, Section 1.2, and US 2006/0268949 A1, U.S. Pat. No. 6,038,055). The resonant enhancement of pulsed radiation is made possible by the frequency comb structure of the spectrum emitted by a mode-locked laser which allows for coupling each individual comb line to a cavity resonance. In the time domain this means that the cavity round trip time corresponds to a multiple of the pulse repetition period. This makes ECs suitable for the enhancement of pulse trains with repetition rates between several MHz and several GHz. Recently, average powers on the order of a few tens of kW have been reached with near-infrared intracavity femtosecond pulses (see A. Cingöz et al. in “Nature” 482, 68-71 (2012), I. Pupeza et al. in “Optics Letters” 35, 2052-2054 (2010), and J. Lee et al. in “Optics Express” 19, 23315-23326 (2011)), owing to advances in amplified laser systems operating in this range of repetition rates. Nowadays, in a cavity focus intensities on the order of 1014 W/cm2 can be readily achieved at repetition rates of several tens of MHz. One of the main motivations for the development of these systems has been the table-top generation of bright coherent extreme ultraviolet (XUV) radiation via high-order harmonic generation (HHG) in a gas (see C. Gohle et al. in “Nature” 436, 234-237 (2005), and R. J. Jones et al. in “Physical Review Letters” 94, 193201 (2005)). Very recently, important new results were achieved in this field, such as record XUV average powers for table-top systems around 20 eV and the first demonstration of radiation with photon energies around 100 eV at repetition rates close to 100 MHz (see I. Pupeza et al. in “Ultrafast Phenomena XVIII”, Proceedings of the 18th International Conference, Lausanne, Switzerland, 2012). These experiments confirm the potential of EC-based HHG and show that a viable way to further increase the photon flux of the generated radiation consists in the increase of the intracavity power level along with the nonlinear interaction volume, i.e. the focus size. This scaling would also benefit other conversion processes, such as THz generation or the generation of hard X-rays via Thomson (inverse-Compton) scattering of the circulating photons from the head-on collision with relativistic electron bunches.
However, while significant progress towards higher average powers and shorter pulse durations has been achieved with high-repetition-rate lasers in recent years, with standard-design femtosecond ECs employing current dielectric laser mirrors, further power scaling is impeded by intensity-related mirror damage. I. Pupeza et al. (“Optics Letters” 35, 2052-2054 (2010)) have described that high intensity is the primary cause of mirror damage. While advances in mirror technology might improve the damage threshold in future, there is an interest in the development of resonators with large spot sizes on the mirrors as an independent solution to this problem, since both the intensity and the thermal gradient at the mirror surface are decreased.
WO 2011/060805 discloses a method of generating high power laser light, wherein the resonator mirrors include plane and parabolic mirrors, which are irradiated by at least one laser light pulse circulating in the enhancement resonator with oblique incidence. Due to the oblique incidence, the area irradiated by the laser beam on the resonator mirror surfaces is increased, thus both the intensity and the thermal gradient on the mirror surfaces are decreased. However, this technique may have disadvantages due to a complex mirror and mirror positioning design and may cause unwanted polarization discrimination effects.
WO 2012/031607 discloses a further method of generating laser light in an EC having a plurality of spherically curved resonator mirrors with a detuned concentric configuration. Contrary to the inherent instability of the concentric resonator, the detuned concentric configuration provides a sufficient stability of the EC, which can be operated close to stability edges resulting in an increased beam radius on the mirrors. Nevertheless, the technique of WO 2012/031607 may have disadvantages in terms of an elliptic beam shape deformation occurring with an increasing beam diameter.
Reducing the peak power by enlarging the beam diameter results in astigmatism effects causing a deformation of the light field along the light path in the EC from a circular cross-section towards an elliptic cross-section. The direction of the ellipticity is predetermined by the cavity configuration. This has a particularly detrimental effect, when the EC is adjusted with enlarged beam diameters and thus operated near the edges of the stability range.